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Conservation and accuracy in meshfree generalized finite difference methods

: Suchde, Pratik
: Klar, A.; Seibold, B.

Volltext urn:nbn:de:0011-n-4940214 (6.0 MByte PDF)
MD5 Fingerprint: 559fb477061bde04c03ed15b901c1b8d
Erstellt am: 9.5.2018

Volltext urn:nbn:de:0011-n-494021-10 (6.0 MByte PDF) - Updated Version
MD5 Fingerprint: 7def3b8f7e5aa2b653c24b67dc14131e
Erstellt am: 30.5.2018

Stuttgart: Fraunhofer Verlag, 2018, XI, 129 S.
Zugl.: Kaiserslautern, TU, Diss., 2018
ISBN: 978-3-8396-1325-2
Dissertation, Elektronische Publikation
Fraunhofer ITWM ()
fluid mechanics; mechanical engineering; Meshfree; accuracy; conservation; FPM; hydrodynamic; angewandte Mathematiker; Berechnungsingenieur; Maschinenbauer; chemischer Ingenieur

The goal of this PhD is to improve various aspects of meshfree Generalized Finite Difference Methods (GFDMs). In this thesis, different meshfree GFDMs are compared, and their potential to solve over-determined problems is presented. A new method is presented that introduces conservation of fluxes in a meshfree setting, which reduces the problem of lack of conservation that has plagued meshfree methods. Special attention is paid on the application of meshfree GFDMs to simulate fluid flow modeled by the incompressible Navier - Stokes equations. A new meshfree GFDM scheme for the same is presented which improves local accuracy, and shows better approximations to the mass conservation condition. Further, different aspects of meshfree Lagrangian frameworks are studied, and new methods to improve accuracy in the Lagrangian movement process are also presented.